Crystal-field Paschen-Back effect on ruby in ultrahigh magnetic fields

Abstract

Zeeman spectra of the R lines of ruby (Cr^{3+}: α-Al_{2}O_{3}) were studied in ultrahigh magnetic fields up to 230 T by magnetophotoluminescence measurements. The observed Zeeman patterns exhibit nonlinear behaviors above 100 T, evidencing the breakdown of the previously reported Paschen-Back effect for B⊥c geometry. We adopted the crystal-field multiplet theory including the cubic crystal field (H_{cubic}), the trigonal crystal field (H_{trig}), the spin-orbit interaction (H_{SO}), and the Zeeman interaction (H_{Z}). It is found that the nonlinear splitting of the R lines is owing to the hybridization between the ^{2}E and ^{2}T_{1} states, which leads to the quantization of these Zeeman levels with the orbital angular momentum. Our results suggest that the exquisite energy balance among H_{cubic}, H_{trig}, H_{SO}, and H_{Z} realized in ruby offers a unique opportunity to observe the onset of the crystal-field Paschen-Back effect toward the high-field extreme.